Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.95.9 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the area of a regular polygon by decomposing it into triangles — one step at a time, with support.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
Regular PolygonSpanish: Polígono regular	A closed flat shape made of straight sides, where every side is the same length and every angle is the same size.	A stop sign is a regular octagon — all 8 sides are the same length and all 8 angles are equal
DecomposeSpanish: Descomponer	To break a shape into smaller, simpler shapes.	Draw lines from the center of a hexagon to each corner → you get 6 equal triangles you can find the area of
TriangleSpanish: Triángulo	A shape with three sides.	Each triangle inside a decomposed hexagon has a base = one side of the hexagon and height = distance from center to side
CompositeSpanish: Compuesto	Made by putting two or more simple shapes together.	6 triangles, each with area 15 sq ft, combine to form a hexagon with total area = 6 × 15 = 90 sq ft
FormulaSpanish: Fórmula	A math rule written with symbols.	For a regular hexagon: Total Area = 6 × (½ × b × h), where b = side length and h = height of each triangle

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A regular hexagon has 6 equal sides. Each side is 6 feet. Each center triangle has a height of 5.2 feet. The height is rounded, so estimate the area.

Split the hexagon into triangles from the center: 6 sides → 6 equal triangles
Find the area of one triangle: 1/2 × 6 × 5.2 = 15.6
Multiply by the number of triangles: 6 × 15.6 = 93.6
The area is about 93.6 square feet.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A regular pentagon splits into 5 equal triangles. Each triangle has a base of 4 cm and a height of 3 cm. The height is rounded, so estimate the area.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

The total area is because one triangle is and there are triangles.

Word bank Regular PolygonDecomposeTriangleCompositeFormulatrianglehalfbaseheightmultiplytotalnumber of sides

Watch outA common mistake

A common mistake in Area of Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area — or adding the number of triangles instead of multiplying. Remember: total area = (one triangle's area) × (number of sides), not (one triangle's area) + (number of sides).

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.95.9 Small Group · Group 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target With my small group, I can find the area of a regular polygon by decomposing it into triangles — one step at a time, with support.

1Complete each step, then write the final answer.
One of the 6 equal triangles from the center.
A regular hexagon has 6 equal sides of 8 cm. Each center triangle has a height of 6.9 cm. The height is rounded, so estimate the area.
1. 1How many equal triangles meet at the center?
2. 2What is the area of one triangle?
3. 3Multiply by 6. What is the area of the hexagon?
Final answer:
2Complete each step, then write the final answer.
A regular octagon has 8 equal sides of 4 in. Each center triangle has a height of 4.8 in. Estimate the area.
1. 1An octagon has 8 sides. How many center triangles does it have?
2. 2What is the area of one triangle?
3. 3What is the area of the octagon?
Final answer:
3Complete each step, then write the final answer.

A square has sides of 6 cm. Lines from its center split it into 4 equal triangles. Each triangle has a height of 3 cm. Find the area using the triangles.
Show your work
Hint Find one triangle: half of base × height. A square has 4 sides, so there are 4 triangles.
Final answer:
4Complete each step, then write the final answer.

A regular pentagon has sides of 8 in. Each center triangle has a height of 5.5 in. Estimate the area of the pentagon.
Show your work
Hint A pentagon has 5 sides, so it splits into 5 equal triangles.
Final answer:
5Complete each step, then write the final answer.

A stop sign is a regular octagon. Each side is 10 in. Each center triangle has a height of 12.1 in. About how much area does the sign have?
Show your work
Hint Find the area of one center triangle. How many triangles does an octagon have?
Final answer:
6Complete each step, then write the final answer.

Leo finds the area of a regular hexagon with sides of 3 cm. Each center triangle has a height of 2.6 cm. He writes 6 × 3 × 2.6 = 46.8. What is the correct area?
Show your work
Hint What is the formula for the area of one triangle? Check what Leo left out.
Final answer:

Explain your thinkingWhy do we multiply one triangle's area by the number of sides? Use Leo's hexagon to explain.

Sentence starter There is one triangle for each ___. · Leo's answer is double because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help